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A geostrophic current in the northern hemisphere features a pressure gradient force directed towards the left of the current (west if the current heads straight north) and Coriolis force directed to the right. For the pressure gradient to be maintained, I can only conclude that the water on the right side of this current must be denser but instead looking at actual data (for example currents between Catalonia and Balearic Islands) it seems to be the opposite. Is my reasoning correct here or are there other circumstances that affect density distribution along currents?

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I believe it makes sense to factor in sea level height. If we assume a northward flow in geostrophic balance (see geostrophic wind) we have \begin{equation} fv = \frac{1}{\rho}\frac{\partial p}{\partial x}. \end{equation}

Using the hydrostatic relation we can replace the term on the right hand side and find

\begin{equation} fv = g\frac{\partial h}{\partial x}, \end{equation} (I assumed constant density $\rho$) or equivalently \begin{equation} \frac{\partial h}{\partial x} = \frac{fv}{g}. \end{equation}

We can conclude that in order to maintain the geostrophic balance the sea level must rise the further we move east.

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